A rise in fragility as a system approaches a tipping point may be sometimes estimated using dynamical indicators of resilience (DIORs) that measure the characteristic slowing down of recovery rates before a tipping point. A change in DIORs could be interpreted as an early warning signal for an upcoming critical transition. However, in order to be able to estimate the DIORs, observational records need to be long enough to capture the response rate of the system. As we show here, the required length of the time series depends on the response rates of the system. For instance, the current rate of anthropogenic climate forcing is fast relative to the response rate of some parts of the climate system. Therefore, we may expect difficulties estimating the resilience from modern time series. So far, there have been no systematic studies of the effects of the response rates of the dynamical systems and the rates of forcing on the detectability trends in the DIORs prior to critical transitions. Here, we quantify the performance of the resilience indicators variance and temporal autocorrelation, in systems with different response rates and for different rates of forcing. Our results show that the rapid rise of anthropogenic forcing to the Earth may make it difficult to detect changes in the resilience of ecosystems and climate elements from time series. These findings suggest that in order to determine with models whether the use of the DIORs is appropriate, we need to use realistic models that incorporate the key processes with the appropriate time constants.

当系统接近临界点时，有时会使用动态恢复力指标（DIOR）估算脆弱性的增加，该指标可测量临界点之前恢复速率下降的特征。DIOR的变化可以解释为即将到来的关键过渡的预警信号。但是，为了能够估计DIOR，观测记录必须足够长才能捕获系统的响应率。正如我们在此处所示，时间序列的所需长度取决于系统的响应率。例如，相对于气候系统某些部分的响应速度，当前的人为气候强迫速度是很快的。因此，我们可能期望从现代时间序列估计弹性方面会遇到困难。至今，尚未有系统研究动力学系统的响应率以及临界转变之前DIOR的强迫率对可探测性趋势的影响。在这里，我们在具有不同响应率和不同强迫率的系统中，量化了回弹指标方差和时间自相关的性能。我们的结果表明，人为强迫对地球的迅速增加可能使从时间序列中检测生态系统和气候要素的复原力变化变得困难。这些发现表明，为了用模型确定DIOR的使用是否合适，我们需要使用将关键过程与适当的时间常数相结合的现实模型。